On Weak bounded negativity conjecture

2024/08/27 by Misra, Snehajit, Ray, Nabanita
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.15187

Abstract

In the first part of this article, we give bounds on self-intersections C² of integral curves C on blow-ups Bl_nX of surfaces X with the anti-cannonical divisor -K_X effective. In the last part, we prove the weak bounded negativity for self-intersections C² of integral curves C in a family of surfaces f:Y\longrightarrow B where B is a smooth curve.

Related

• Weak Bounded Negativity Conjecture
• Towards bounded negativity of self-intersection on general blown-up\n projective planes
• Self-intersection Number of Negative Curves on Fermat Surfaces
• Unbounded negativity on rational surfaces in positive characteristic
• Bounded negativity and Harbourne constants on ruled surfaces